Ch 32: AC Circuits

Knight Calc - Physics for Scientists and Engineers 5th Edition

Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796당신이 사용하는 게 아니라요?교과서 변경

Knight Calc 5th Edition

Ch 32: AC Circuits

문제 42a

32장, 문제 42a

What is the peak current supplied by the emf in FIGURE P32.42?

검증된 단계별 안내

Identify the components of the circuit in FIGURE P32.42. Typically, such problems involve an AC circuit with a resistor, inductor, and/or capacitor. Note the values of resistance (R), inductance (L), capacitance (C), and the peak voltage of the emf (V₀).

Understand that the peak current (I₀) in an AC circuit is determined by the relationship:

I

₀=V₀Z, where

Z

is the impedance of the circuit.

Calculate the impedance

Z

of the circuit. For a series RLC circuit, the impedance is given by:

Z = \sqrt{R^{2} + (^{X}}

_L-X_C)2, where

X

_L=ωL is the inductive reactance and

X

_C=1ωC is the capacitive reactance. Here,

ω = 2 π f

is the angular frequency of the AC source.

Substitute the given values of resistance, inductance, capacitance, and frequency into the formulas for

X

_L,

X

_C, and

Z

. Simplify the expressions to find the total impedance of the circuit.

Finally, use the formula

I

₀=V₀Z to calculate the peak current. Substitute the peak voltage of the emf and the calculated impedance into the equation to determine the peak current.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Electromotive Force (emf)

Electromotive force (emf) is the voltage generated by a source, such as a battery or generator, when no current is flowing. It represents the energy per unit charge provided by the source to move charges through a circuit. Understanding emf is crucial for analyzing how much current can be supplied under different circuit conditions.

Ohm's Law

Ohm's Law states that the current (I) flowing through a conductor between two points is directly proportional to the voltage (V) across the two points and inversely proportional to the resistance (R) of the conductor. This relationship is expressed as I = V/R. It is fundamental for calculating the peak current in a circuit when the emf and resistance are known.

Peak Current

Peak current refers to the maximum instantaneous current that can flow in a circuit when the voltage is at its highest point. In the context of an emf source, it is determined by the source's voltage and the total resistance in the circuit. Understanding peak current is essential for assessing the performance and safety of electrical systems.